P u ,t , P u ,t−1 Power generation of generator u at t and t − 1, respectively.Power from bus b to bus b at t. P S n,t , P S n ,t Pressure of gas nodes n and n at t. o u ,t Binary variable to indicate if generator u is started up at t. θ b,t , θ b ,t Phase angles of buses b and b at t. η k p ,t , η k p,tBinary variables to indicate if the piecewise linear function k is selected. '1' denotes 'selected', and '0' denotes 'nonselected'. π n,t , π n ,t